In an appearance of "Fox and Friends" on Tuesday, the Fox anchor singled out Stelter among numerous media figures whom Hannity accused of being "in the tank" for Democratic presidential nominee Hillary Clinton, including former Time Inc. CEO John Huey. A past fellow at the Shorestein Center, part of Harvard's Kennedy School of Government, Huey was a guest on Stelter's "Reliable Sources" show on Sunday.

"You've got this little pipsqueak named Brian Stelter," Hannity said. "And he allowed this arrogant professor from the Kennedy School of Journalism to talk about Trump being a demagogue and demagogues like Trump becoming dictators."

He added: "That's the type of coverage that CNN offers in this presidential race."

The Fox News host then said the news media was doubling up against Trump and the press "literally kisses Hillary Clinton's ass and Obama's ass every day."

In the past month, Stelter has repeatedly criticized Hannity's willingness to give significant airtime to baseless and unproven theories about Clinton's health and whether the election is rigged. On Sunday's episode of "Reliable Sources," the CNN anchor criticized Hannity for bringing on doctors to watch clips of Clinton and speculate about potential health issues.

"That was reckless speculation by Sean Hannity. All of it," Stelter said.

"Hannity is not interested in the truth about Clinton's health. If he was, he could've interviewed people who were actually there during the episodes that he's exploiting."